Electrons In Germanium Research Articles

Anisotropy of warm electrons in germanium and silicon

Measurements of the warm carrier coefficient β, which describes the deviations from Ohm's law at medium electric field strengths, are reported forn-type silicon andn-type germanium for different impurity concentrations and for different crystallographic orientations. Due to the anisotropy of β we can divide into deviations from Ohm's law in one valley of the many valley-semiconductors and into intervalley scattering between the different valleys. Both effects decrease with increasing electron concentration. Additional we observe a maximum in intervalley scattering with the inset of dominating impurity scattering.

6.—Electron Diffraction and Electron Mobility in Non-polar Crystals

SynopsisIt is shown that the mobility of electrons in silicon or germanium can be estimated in a relatively simple manner. The scattering scross-section of a ’beam’ of electrons in the conduction band is evaluated in the same way as for a beam of X-rays or of slow neutrons which is scattered by phonons. It therefore involves the atomic scattering factor for electrons rather than the deformation potential introduced by Bardeen and Shockley. Predicted mobilities are in satisfactory agreement with observation.

Negative differential mobility of electrons in germanium: A Monte Carlo calculation of the distribution function, drift velocity and carrier population in the (111) and (100) minima

Hot electron transport properties in germanium have been investigated using a Monte Carlo method with the principal objective of elucidating the origin of the negative differential mobility observed at low temperatures and high electric fields. The model takes full account of electron transfer from the (111) to the (100) valleys and incorporates the ellipsoidal constant energy surfaces associated with both these sets of minima. The scattering rates within the (111) valleys are determined from low field data, while constraints are placed on the strength of the scattering to and within the (100) valleys by recent data on the variation of low field resistivity with pressure. It is demonstrated that this model can give a consistent explanation of the magnitude of the negative differential mobility and its threshold field as functions of temperature orientation, uniaxial stress and hydrostatic pressure. The relative importance of f((100) from or to (010)) and g((100) from or to (100)) scattering in the (100) valleys is discussed in relation to uniaxial stress experiments and it is concluded that g scattering must be an important process.

326. Inelastic scattering of slow electrons in germanium and silicon: V L Borisov and Yu I Kazeev, Fiz Tverd Tela, 12 (7), July 1970, 2186–2187 ( in Russian)

326. Inelastic scattering of slow electrons in germanium and silicon: V L Borisov and Yu I Kazeev, Fiz Tverd Tela, 12 (7), July 1970, 2186–2187 ( in Russian)

Deformation Potential Constants for Electrons in Silicon and Germanium from Cyclotron Resonance Experiments

Deformation Potential Constants for Electrons in Silicon and Germanium from Cyclotron Resonance Experiments

Galvanomagnetic effects of hot electrons in n-type germanium

Numerical calculations of the magnetoconductivity of n-Ge in the 〈 100〉 and 〈 111〉 crystallographic directions were performed at 80°K and for field strength up to 5 kV/cm. It is shown that it is necessary to consider the dependence of the population of different valleys on the magnetic field in order to get agreement with experimental results.

Magnetoresistance and Hall Effect of Hot Electrons in Germanium and Carrier Transfer to Higher Minima

Measurements are reported of the Hall coefficient and the ratio of longitudinal over transverse magnetoresistance in $n$-type Ge up to electric field strengths of 3 and 9 kV/cm, respectively, for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{j}}\ensuremath{\parallel}[100]$ at 200\ifmmode^\circ\else\textdegree\fi{}K, in order to obtain quantitative information about electron transfer to higher conduction-band minima. The lattice temperature was high enough to ensure that no negative differential conductivity was present. Calculations of the galvanomagnetic properties have been performed for the case that (i) electrons are only in the normally occupied $〈111〉$ valleys, taking into account acoustical, optical, and equivalent intervalley scattering as well as scattering by ionized impurities; and (ii) electrons are transferred to the higher $〈100〉$ conduction-band minima. Only in case (ii) is reasonable agreement between theoretical and experimental results obtained, giving a mobility ratio of only about 4. This is of the same order of magnitude as the theoretical value by Paige.

The velocity-field characteristic of electrons in Ge under uniaxial pressure

The velocity-field characteristic of electrons in germanium under uniaxial pressure has been measured. It is shown that negative differential mobility exists at high pressures, in agreement with recent observations of Gunn-oscillations in this material.

Temperature Dependence of Acoustic-Phonon Attenuation by Bound Donor Electrons in Germanium

In the present work it has been shown that the discrepancy between Kwok's theory and the observed temperature dependence of acoustic-phonon attenuation in P-doped Ge beyond its maximum can be partially explained if one modifies Kwok's theory to include the transitions to singlet and triplet states from higher-energy states which may be relevant at higher temperatures. This work confirms that Kwok's theory overestimates phonon attenuation in the higher-temperature region.

MEASUREMENT OF THE VELOCITY FIELD CHARACTERISTIC OF ELECTRONS IN GERMANIUM

The velocity field characteristics of electrons in germanium were measured in a range of temperatures between 33°K and 130°K and the electric field along the 〈 100 〉 orientation of the crystal. At 33°K a negative differential mobility of 300 cm2/V-sec was observed with a threshold field of 1.5 kV/cm. The negative differential mobility decreases with increasing temperature. At 130°K there is definitely no negative differential mobility.

On the solution of the effective-mass equation for conduction electrons in germanium and silicon

A new perturbation method is proposed for obtaining approximate solutions to the effective mass equation for conduction electrons in a many-valley semiconductor.

On the solution of the effective-mass equation for conduction electrons in germanium and silicon

On the solution of the effective-mass equation for conduction electrons in germanium and silicon

Measurement of the Energy Loss of Germanium Atoms to Electrons in Germanium at Energies below 100 keV. II

The amount of energy lost in the production of hole-electron pairs by germanium atoms stopping in a germanium crystal has been measured at energies of 56.2 and 102.9 keV. Inelastic neutron scattering in a Ge(Li) gamma-ray detector was used to produce the 690-keV ${\mathrm{Ge}}^{72}$ state and the 596-keV ${\mathrm{Ge}}^{74}$ state. The lines corresponding to the de-excitation of these states were broadened by summing with the hole-electron pairs produced by the recoiling Ge atom. A particular recoil energy was selected by requiring a coincidence with the outgoing inelastically scattered neutron, which was detected by a stilbene recoil counter placed at either 90\ifmmode^\circ\else\textdegree\fi{} or 150\ifmmode^\circ\else\textdegree\fi{} to the incident neutron beam. The results of the present experiment confirm a previous investigation by Chasman, Jones, and Ristinen and do not agree with the published results of Sattler, Vook, and Palms.

Many-Valley Dipole Scattering of Electrons in Germanium and Silicon

The theory of dipole scattering is developed for germanium and silicon, whose conduction-band structure can be described by a simple many-valley model. A formalism is used which employs a linear approximation to the distribution function, and is due to Herring and Vogt. It is shown that, in the approximation, an alternative approach due to Samoilovich et al. gives an identical result. The relaxation-time ratio $\frac{{\ensuremath{\tau}}_{\ensuremath{\parallel}}}{{\ensuremath{\tau}}_{\ensuremath{\perp}}}$ is computed as a function of energy and it is shown analytically that, as $E\ensuremath{\rightarrow}\ensuremath{\infty}$, $\frac{{\ensuremath{\tau}}_{\ensuremath{\parallel}}}{{\ensuremath{\tau}}_{\ensuremath{\perp}}}\ensuremath{\rightarrow}3.69$. This is approximately the square root of the corresponding result for point ions. Thus the scattering due to dipoles is less sensitive to the anistropy of the energy surfaces than in the point-ion case. This can be explained by considering the form of the cross sections presented by each type of scattering center. Finally, some numerical work on the mobility and the effective anisotropy parameter is presented.

HELICONS IN n-TYPE SILICON AND GERMANIUM

Using the self-consistent field method, the collective modes of the electrons in n-type silicon and germanium in a constant external magnetic field are calculated from the frequency- and wavelength-dependent conductivity tensor σ(ω, q) for simple symmetry directions. Because of the differing orientations of the longitudinal axes of the energy surfaces relative to the direction of the external field, there is, in general, more than one carrier involved, with the result that the helicon spectrum can have more than one branch. The minimum frequencies of the higher ("optical") branches depend on the effective mass parameters in a different way than do the cyclotron resonance frequencies. The frequency spectra of all collective modes are discussed in the long-wavelength limit.

Measurement of the Energy Loss of Germanium Atoms to Electrons in Germanium at Energies Below 100 keV

Measurement of the Energy Loss of Germanium Atoms to Electrons in Germanium at Energies Below 100 keV

Measurement of the Energy Loss of Germanium Atoms to Electrons in Germanium at Energies Below 100 keV

Measurement of the Energy Loss of Germanium Atoms to Electrons in Germanium at Energies Below 100 keV

Influence of non-equivalent inter-valley scattering on hot-electron effects in germanium

The drift velocity of electrons in germanium exhibits a pronounced saturation effect at electric field strengths between 3 kV/cm and 10 kV/cm. This effect has been explained by a simple theoretical model where the energy relaxation is supposed to be dominated by optical phonon scattering. It is shown that a consistent treatment should include energy relaxation through acoustical phonon scattering. This, however, destroys the saturation of the drift velocity. Also the mean free paths calculated from this model are an order of magnitude higher than those found from experiments on avalanche effect. It is suggested that the additional scattering needed is due to the non-equivalent inter-valley scattering between 〈111〉 valleys and 〈100〉 valleys. Numerical results from optical experiments and pressure experiments support this model.

Open-base Breakdown in Diffused N-P-N Junction Transistors†

ABSTRACT A one-dimensional analysis is presented on the open-base breakdown characteristics of diffused n-p-n transistors. From breakdown voltage measurements upon selected devices—in conjunction with breakdown voltage calculations—‘ effective ’ values are established for the ionization rate of electrons in germanium and silicon p-n junctions, when biased substantially below avalanche breakdown. These ‘ effective ’ electron ionization rates are used to calculate the open-base breakdown voltage for transistors exhibiting a large collector punch-through voltage ; such calculations are graphically illustrated throughout iv range of parameters applicable to many practical situations. A discussion is also presented on the influence of an abrupt conductivity increase within the collector junction space-charge layer, of the typo encountered in an idealized epitaxial structure.

Some remarks on microwave excitation of dc by hot electrons in germanium

Some remarks on microwave excitation of dc by hot electrons in germanium